One of the most important recent discoveries in cosmology--and science in general--is that the expansion rate of the universe is not staying steady or getting slower, as most scientists had assumed; on the contrary, it is accelerating. Something is counteracting gravity and making it so that in billions of years, the universe will be an even vaster, emptier realm, filled with stars and galaxies flickering out one by one until there is only darkness. In this book, Livio, a senior scientist at Baltimore's Space Telescope Science Institute, evaluates current theories about the universe in terms of whether or not they are ""beautiful."" Livio defines beauty for purely scientific purposes: a beautiful scientific theory, he explains, must be symmetric and simple (reductionist), and it must follow the Copernican principle that man is not the center of the universe--it need not be elegant. Livio's discussion, however, carefully constructed (like a well-laid-out mathematical proof), certainly is elegant. Readers who only hazily remember high school math and science classes will enjoy the author's clear, jargon-free explanation of such complicated astronomical concepts as inflationary theory, ""pocket"" or multiple universes and the anthropic principle. Although the opening chapters are weighed down with extraneous references to art and literature, once Livio gets into his subject, he employs such references more selectively. Any educated individual interested in current theories about the past and future of the universe will want to read this lucid book. 10 b&w photos and drawings. (Mar.)